C(14,6,2) = 7

Method of Construction: simple construction: multiple of smaller covering

 1  2  3  8  9 10 
 1  4  5  8 11 12 
 1  6  7  8 13 14 
 2  4  6  9 11 13 
 2  5  7  9 12 14 
 3  4  7 10 11 14 
 3  5  6 10 12 13